In allometric studies, the joint distribution of the log-transformed morphometric variables is typically symmetric and with heavy tails. Moreover, in the bivariate case, it is customary to explain the morphometric variation of these variables by fitting a convenient line, as for example the first principal component (PC). To account for all these peculiarities, we propose the use of multiple scaled symmetric (MSS) distributions. These distributions have the advantage to be directly defined in the PC space, the kind of symmetry involved is less restrictive than the commonly considered elliptical symmetry, the behavior of the tails can vary across PCs, and their first PC is less sensitive to outliers. In the family of MSS distributions, we also propose the multiple scaled shifted exponential normal distribution, equivalent of the multivariate shifted exponential normal distribution in the MSS framework. For the sake of parsimony, we also allow the parameter governing the leptokurtosis on each PC, in the considered MSS distributions, to be tied across PCs. From an inferential point of view, we describe an EM algorithm to estimate the parameters by maximum likelihood, we illustrate how to compute standard errors of the obtained estimates, and we give statistical tests and confidence intervals for the parameters. We use artificial and real allometric data to appreciate the advantages of the MSS distributions over well-known elliptically symmetric distributions and to compare the robustness of the line from our models with respect to the lines fitted by well-established robust and non-robust methods available in the literature.
We have previously derived power calculation formulas for cohort studies and clinical trials using the longitudinal mixed effects model with random slopes and intercepts to compare rate of change across groups [Ard & Edland, Power calculations for clinical trials in Alzheimer’s disease. J Alzheim Dis 2011;21:369–77]. We here generalize these power formulas to accommodate 1) missing data due to study subject attrition common to longitudinal studies, 2) unequal sample size across groups, and 3) unequal variance parameters across groups. We demonstrate how these formulas can be used to power a future study even when the design of available pilot study data (i.e., number and interval between longitudinal observations) does not match the design of the planned future study. We demonstrate how differences in variance parameters across groups, typically overlooked in power calculations, can have a dramatic effect on statistical power. This is especially relevant to clinical trials, where changes over time in the treatment arm reflect background variability in progression observed in the placebo control arm plus variability in response to treatment, meaning that power calculations based only on the placebo arm covariance structure may be anticonservative. These more general power formulas are a useful resource for understanding the relative influence of these multiple factors on the efficiency of cohort studies and clinical trials, and for designing future trials under the random slopes and intercepts model.
Gradient boosting from the field of statistical learning is widely known as a powerful framework for estimation and selection of predictor effects in various regression models by adapting concepts from classification theory. Current boosting approaches also offer methods accounting for random effects and thus enable prediction of mixed models for longitudinal and clustered data. However, these approaches include several flaws resulting in unbalanced effect selection with falsely induced shrinkage and a low convergence rate on the one hand and biased estimates of the random effects on the other hand. We therefore propose a new boosting algorithm which explicitly accounts for the random structure by excluding it from the selection procedure, properly correcting the random effects estimates and in addition providing likelihood-based estimation of the random effects variance structure. The new algorithm offers an organic and unbiased fitting approach, which is shown via simulations and data examples.
This work reports the preparation, characterization, and a drug release study of mesoporous silica nanoparticles (MNPSiO2) functionalized with folic acid (FA) and loaded with Cis-Pt as a targeted release system to kill glioblastoma cancer cells. The MNPSiO2 were synthesized by the Stöber method using hexadecyltrimethylammonium bromide as the templating agent, which was finally removed by calcination at 550°C. The folic acid was chemically anchored to the silica nanoparticles surface by a carbodiimide reaction. Several physicochemical techniques were used for the MNPSiO2 characterization, and a triplicate in vitro Cis-Pt release test was carried out. The release Cis-Pt experimental values were fitted to different theoretical models to find the Cis-Pt release mechanism. The cytotoxicity evaluation of the MNPSiO2 was performed using LN 18 cells (human GBM cells). Homogeneous and well-defined nanoparticles with well-distributed and homogeneous porosity were obtained. The spectroscopic results show the proper functionalization of the mesoporous nanoparticles; besides, MNPSiO2 showed high surface area and large pore size. High correlation coefficients were obtained. Though the best fitted was the Korsmeyer-Peppas kinetic model, the Higuchi model adjusted better to the results obtained for our system. The MNPSiO2-FA were highly biocompatible, and they increased the cytotoxic effect of Cis-Pt loaded in them.
Metals with a bimodal grain size distribution have been found to have both high strength and good ductility. However, the coordinated deformation mechanisms underneath the ultrafine-grains (UFGs) and coarse grains (CGs) still remain undiscovered yet. In present work, we reported grain coarsening and detwinning in a bimodal Cu under tensile deformation. Mechanically induced grain coarsening and detwinning have been reported in nanocrystalline metals. However, it was first observed that grain coarsening existed in a wide grain size distribution from 350 nm to 1 µm. The underlying deformation mechanisms for grain coarsening and detwinning were analyzed and discussed.
The two one-sided t-tests (TOST) method is the most popular statistical equivalence test with many areas of application, i.e., in the pharmaceutical industry. Proper sample size calculation is needed in order to show equivalence with a certain power. Here, the crucial problem of choosing a suitable mean-difference in TOST sample size calculations is addressed. As an alternative concept, it is assumed that the mean-difference follows an a-priori distribution. Special interest is given to the uniform and some centered triangle a-priori distributions. Using a newly developed asymptotical theory a helpful analogy principle is found: every a-priori distribution corresponds to a point mean-difference, which we call its Schuirmann-constant. This constant does not depend on the standard deviation and aims to support the investigator in finding a well-considered mean-difference for proper sample size calculations in complex data situations. In addition to the proposed concept, we demonstrate that well-known sample size approximation formulas in the literature are in fact biased and state their unbiased corrections as well. Moreover, an R package is provided for a right away application of our newly developed concepts.
Semi-Markov models are widely used for survival analysis and reliability analysis. In general, there are two competing parameterizations and each entails its own interpretation and inference properties. On the one hand, a semi-Markov process can be defined based on the distribution of sojourn times, often via hazard rates, together with transition probabilities of an embedded Markov chain. On the other hand, intensity transition functions may be used, often referred to as the hazard rates of the semi-Markov process. We summarize and contrast these two parameterizations both from a probabilistic and an inference perspective, and we highlight relationships between the two approaches. In general, the intensity transition based approach allows the likelihood to be split into likelihoods of two-state models having fewer parameters, allowing efficient computation and usage of many survival analysis tools. Nevertheless, in certain cases the sojourn time based approach is natural and has been exploited extensively in applications. In contrasting the two approaches and contemporary relevant R packages used for inference, we use two real datasets highlighting the probabilistic and inference properties of each approach. This analysis is accompanied by an R vignette.